24,902 research outputs found
A hierarchical Bayesian model for predicting ecological interactions using scaled evolutionary relationships
Identifying undocumented or potential future interactions among species is a
challenge facing modern ecologists. Recent link prediction methods rely on
trait data, however large species interaction databases are typically sparse
and covariates are limited to only a fraction of species. On the other hand,
evolutionary relationships, encoded as phylogenetic trees, can act as proxies
for underlying traits and historical patterns of parasite sharing among hosts.
We show that using a network-based conditional model, phylogenetic information
provides strong predictive power in a recently published global database of
host-parasite interactions. By scaling the phylogeny using an evolutionary
model, our method allows for biological interpretation often missing from
latent variable models. To further improve on the phylogeny-only model, we
combine a hierarchical Bayesian latent score framework for bipartite graphs
that accounts for the number of interactions per species with the host
dependence informed by phylogeny. Combining the two information sources yields
significant improvement in predictive accuracy over each of the submodels
alone. As many interaction networks are constructed from presence-only data, we
extend the model by integrating a correction mechanism for missing
interactions, which proves valuable in reducing uncertainty in unobserved
interactions.Comment: To appear in the Annals of Applied Statistic
Prioritizing Populations for Conservation Using Phylogenetic Networks
In the face of inevitable future losses to biodiversity, ranking species by conservation priority seems more than prudent. Setting conservation priorities within species (i.e., at the population level) may be critical as species ranges become fragmented and connectivity declines. However, existing approaches to prioritization (e.g., scoring organisms by their expected genetic contribution) are based on phylogenetic trees, which may be poor representations of differentiation below the species level. In this paper we extend evolutionary isolation indices used in conservation planning from phylogenetic trees to phylogenetic networks. Such networks better represent population differentiation, and our extension allows populations to be ranked in order of their expected contribution to the set. We illustrate the approach using data from two imperiled species: the spotted owl Strix occidentalis in North America and the mountain pygmy-possum Burramys parvus in Australia. Using previously published mitochondrial and microsatellite data, we construct phylogenetic networks and score each population by its relative genetic distinctiveness. In both cases, our phylogenetic networks capture the geographic structure of each species: geographically peripheral populations harbor less-redundant genetic information, increasing their conservation rankings. We note that our approach can be used with all conservation-relevant distances (e.g., those based on whole-genome, ecological, or adaptive variation) and suggest it be added to the assortment of tools available to wildlife managers for allocating effort among threatened populations
Uncovering latent structure in valued graphs: A variational approach
As more and more network-structured data sets are available, the statistical
analysis of valued graphs has become common place. Looking for a latent
structure is one of the many strategies used to better understand the behavior
of a network. Several methods already exist for the binary case. We present a
model-based strategy to uncover groups of nodes in valued graphs. This
framework can be used for a wide span of parametric random graphs models and
allows to include covariates. Variational tools allow us to achieve approximate
maximum likelihood estimation of the parameters of these models. We provide a
simulation study showing that our estimation method performs well over a broad
range of situations. We apply this method to analyze host--parasite interaction
networks in forest ecosystems.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS361 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Topology Discovery of Sparse Random Graphs With Few Participants
We consider the task of topology discovery of sparse random graphs using
end-to-end random measurements (e.g., delay) between a subset of nodes,
referred to as the participants. The rest of the nodes are hidden, and do not
provide any information for topology discovery. We consider topology discovery
under two routing models: (a) the participants exchange messages along the
shortest paths and obtain end-to-end measurements, and (b) additionally, the
participants exchange messages along the second shortest path. For scenario
(a), our proposed algorithm results in a sub-linear edit-distance guarantee
using a sub-linear number of uniformly selected participants. For scenario (b),
we obtain a much stronger result, and show that we can achieve consistent
reconstruction when a sub-linear number of uniformly selected nodes
participate. This implies that accurate discovery of sparse random graphs is
tractable using an extremely small number of participants. We finally obtain a
lower bound on the number of participants required by any algorithm to
reconstruct the original random graph up to a given edit distance. We also
demonstrate that while consistent discovery is tractable for sparse random
graphs using a small number of participants, in general, there are graphs which
cannot be discovered by any algorithm even with a significant number of
participants, and with the availability of end-to-end information along all the
paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is
scheduled to appear in J. on Random Structures and Algorithm
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